M1,M2/G/1/K,∞ retrial queue with two types of calls

Abstract

As a mathematical model of a modern telephone exchange, we consider retrial queue with two types of customers. If an arriving customer finds the server idle, he immediately receives service. In the case of blocking due to busy server, type I customers can be queued whereas type II customers retry for service after random amount of time. It is very practical toassume that there are only finite wating positions for type I customers. When the waiting place is full, an arriving type I customer is lost. In this thesis, we analyze the retrial queue with two types of customers where the capacity of waiting place for type I customers is finite. We find out the joint probability generating functions of the number of customers in the system by the suppoementary variable method.